Online Health Management for Complex Nonlinear Systems Based on Hidden Semi-Markov Model Using Sequential Monte Carlo Methods

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left">Observation time point (<svg height="12.4375" id="M219" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 4.6999998 12.4375" width="4.6999998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M238 681l-124 -585q-7 -31 4 -31q10 0 37.5 18.5t49.5 41.5l16 -22q-40 -48 -89.5 -81.5t-76.5 -33.5q-42 0 -16 122l105 488q7 32 0 41t-39 9h-35l5 26q35 3 71 13t58 17.5t26 7.5q14 0 8 -31z" id="x1D459"></path></g>
</svg>)</td><td align="center">State probability</td><td align="center">Health state</td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left">1</td><td align="center">0.8821</td><td align="center" rowspan="5"><span style="width: 12.8375px;"><svg height="11.825" id="M220" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 12.8375 11.825" width="12.8375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><use xlink:href="#x1D460"></use></g>
<g transform="matrix(.012,-0,0,-.012,6.438,11.762)"><use xlink:href="#x31"></use></g>
</svg></span></td></tr><tr><td align="left">2</td><td align="center">0.8556</td></tr><tr><td align="left">3</td><td align="center">0.7908</td></tr><tr><td align="left">4</td><td align="center">0.7744</td></tr><tr><td align="left">5</td><td align="center">0.6379</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

State density of 5 observation time points.

Mathematical Problems in Engineering

tab3

Table 3

Table 3: Online Health Management for Complex Nonlinear Systems Based on Hidden Semi-Markov Model Using Sequential Monte Carlo Methods 